# Online optimisation for dynamic electrical impedance tomography

arXiv: https://arxiv.org/abs/2412.12944 · HTML: https://mlsanity.com/paper/2412.12944/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 59 references that are in the map.
- First posted on arXiv 17 Dec 2024.

## Builds on (most cited first, 22 of 22)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Learning: A Modern Introduction Using Convex Optimization](https://mlsanity.com/paper/1912.13213/) (2019)
- [Dynamical Models and Tracking Regret in Online Convex Programming](https://mlsanity.com/paper/1301.1254/) (2013)
- [Time-Varying Convex Optimization: Time-Structured Algorithms and Applications](https://mlsanity.com/paper/2006.08500/) (2020)
- [Online Proximal-ADMM For Time-varying Constrained Convex Optimization](https://mlsanity.com/paper/2005.03267/) (2020)
- [Online Primal-Dual Methods with Measurement Feedback for Time-Varying Convex Optimization](https://mlsanity.com/paper/1804.05159/) (2018)
- [Ensemble Kalman Methods With Constraints](https://mlsanity.com/paper/1901.05668/) (2019)
- [Regrets of Proximal Method of Multipliers for Online Non-convex Optimization with Long Term Constraints](https://mlsanity.com/paper/2204.10986/) (2022)
- [A primal-dual hybrid gradient method for non-linear operators with applications to MRI](https://mlsanity.com/paper/1309.5032/) (2013)
- [Online convex optimization and no-regret learning: Algorithms, guarantees and applications](https://mlsanity.com/paper/1804.04529/) (2018)
- [Running Primal-Dual Gradient Method for Time-Varying Nonconvex Problems](https://mlsanity.com/paper/1812.00613/) (2018)
- [Distributed Online Convex Optimization with Improved Dynamic Regret](https://mlsanity.com/paper/1911.05127/) (2019)
- [Online Gradient Descent for Linear Dynamical Systems](https://mlsanity.com/paper/1912.09311/) (2019)
- [Testing and non-linear preconditioning of the proximal point method](https://mlsanity.com/paper/1703.05705/) (2017)
- [Predictive online optimisation with applications to optical flow](https://mlsanity.com/paper/2002.03053/) (2020)
- [A nonsmooth primal-dual method with interwoven PDE constraint solver](https://mlsanity.com/paper/2211.04807/) (2022)
- [Differential estimates for fast first-order multilevel nonconvex optimisation](https://mlsanity.com/paper/2412.01481/) (2024)
- [Acceleration and global convergence of a first-order primal--dual method for nonconvex problems](https://mlsanity.com/paper/1802.03347/) (2018)
- [Relaxed Gauss-Newton methods with applications to electrical impedance tomography](https://mlsanity.com/paper/2002.08044/) (2020)
- [Mumford-Shah regularization in electrical impedance tomography with complete electrode model](https://mlsanity.com/paper/2110.15697/) (2021)
- [Bayesian Spatiotemporal Modeling for Inverse Problems](https://mlsanity.com/paper/2204.10929/) (2022)
- [Prediction techniques for dynamic imaging with online primal-dual methods](https://mlsanity.com/paper/2405.02497/) (2024)

## Abstract (arXiv)

Online optimisation studies the convergence of optimisation methods as the data embedded in the problem changes. Based on this idea, we propose a primal dual online method for nonlinear time-discrete inverse problems. We analyse the method through regret theory and demonstrate its performance in real-time monitoring of moving bodies in a fluid with Electrical Impedance Tomography (EIT). To do so, we also prove the second-order differentiability of the Complete Electrode Model (CEM) solution operator on L^∞.